2024 LC Thread: Name That Tune

or, or…he knows he can get negative engagement from us math losers and he’s an evil meathead savant

https://x.com/historycalendar/status/1841160634857374147

14 Likes

They are both probability of success in two tries, don’t need a YouTube video for that :smiley:

In before someone tells me I’m horribly wrong and I should’ve watched

Coates boils it down so well. Worth watching for final 2 min. Just cuts through all the crap and nails it.

His book comes to my house tmw I think, can’t wait to read it

1 Like

Me too.

I first saw this a while back. Even when shown the solution it took me a while to get it. What you posted is a better explanation than what I remember reading.

Not really a fan but it popped on my feed which is where I got it from. I didn’t really believe it until I started looking at it myself.

So what are the chances each gets above .50? Square root is clear, 75% chance. Two dice being thrown again it is clear there is a 75% chance…hmm

Lets look at the chance each gets above .60. Square root clear chance there is a 64% chance. For two random numbers there is a (1-.4)(1-.4) chance it won’t be greater than .60, which is the same thing.

You can expand this further. Cube root of one die equal max of three die, and so on.

1 Like

maybe it’s already clear to everyone who understood this, but just in case, all that you need is to pick a random threshold R, in such a way that you have positive probability of landing into any given interval (technical word for saying this is that the measure has full support). Taking a(ny) Gaussian works, but there’s of course a lot of other measures that have this property.

Yeah the cdfs for both reduce to the form F(x) = x^n, which might be surprising if you’ve never thought about the distribution of order statistics for uniform random variables. For Xi ~ U(0,1), they follow a beta distribution. It’s noteworthy because these rarely work out nicely. The maximum is distributed Beta(n,1), so if you try Beta(2,1) in this applet you’ll generate the same pdf plot he shows in the video, or try other values of n for more “dice.”

https://www.acsu.buffalo.edu/~adamcunn/probability/beta.html

1 Like

7 Likes

Nullify

1 Like

Agreed. Not clear why they arrested him.

The meth probably had something to do with it.

1 Like

Duane Johnson was arrested without incident and was charged with criminal neglect and felony counts of theft and receiving stolen property. His bond was set to $250,000 or $150,000 with conditions.

Lots of stolen guns, apparently.

1 Like

Or maybe the cops are lying about that.

Several guns and hundreds of rounds is nothing in America. This guy is being railroaded.

Guy sounds solid as The Rock

6 Likes

It was 47 guns.

They say that dude is 58. I guess meth added 25 years.

Eh, cops probably lying about everything.